Salt-Induced Diffusion of Star and Linear Polyelectrolytes within Multilayer Films

This study explores the effect of salt on the diffusivity of polyelectrolytes of varied molecular architecture in layer-by-layer (LbL) films in directions parallel and perpendicular to the substrate using fluorescence recovery after photobleaching (FRAP) and neutron reflectivity (NR) techniques, respectively. A family of linear, 4-arm, 6-arm, and 8-arm poly(methacrylic acids) (LPMAA, 4PMAA, 6PMAA, and 8PMAA, respectively) of matched molecular weights were synthesized using atom transfer radical polymerization and assembled with a linear polycation, poly[2-(trimethylammonium)ethyl methacrylate chloride] (QPC). NR studies involving deuterated QPC revealed ∼10-fold higher polycation mobility for the 8PMAA/QPC system compared to all-linear LbL films upon exposure to 0.25 M NaCl solutions at pH 6. FRAP experiments showed, however, that lateral diffusion of star PMAAs was lower than LPMAA at NaCl concentrations below ∼0.22 M NaCl, with a crossover to higher mobility of star polymers in more concentrated salt solutions. The stronger response of diffusion of star PMAA to salt is discussed in the context of several theories previously suggested for diffusivity of polyelectrolyte chains in multilayer films and coacervates.

Ridge, Tennessee 37831, USA Fig. S1.ARGET ATRP polymerization of TBMA using a EtBiB ATRP initiator: (A) GPC traces at different polymerization times and (B) time evolution of ln[M] 0 /[M] t during synthesis of linear PTBMA.The red line represents the fit of the data using the equation , where is increase of the film thickness at time t, is increase of the film thickness at the equilibrium state,  ∞  1 is a characteristic constant, t is time and n is the exponent that describes the diffusion type. 3he fitting parameters are shown in Table S1.(A) and (QPC/6PMAA) 2 /(QPC/6PMAA*) 3 /(QPC/6PMAA) 2 (B) films deposited at pH 6 in 0.01 M phosphate buffer, bleached at 0.1 mW and monitored at 1μW when exposed to 0.125 M (diamonds), 0.17 M (up triangles), 0.21 M (circles) and 0.25 M (squares) NaCl solutions.The solid lines represent the exponential fit to the data.

Fitting Model for Neutron Reflectometry Data
We implemented the model previously used for analyzing the neutron data. 1,2 n this model, we fitted the thickness and internal width of the hydrogenated and deuterated stacks (H-and D-stack respectively) as independent paraments, and scattering length density (SLD) of the stacks were parameterized by the fitting of film density, water content, ratio of polyanion to polycation and the intermixing between the stacks.Note that fitted internal roughness (Table S3-S21) are given as full width at half-maximum and are decreased by a factor 2.35 to get a Gaussian width that is used for the calculation of diffusion coefficients.
The SLD of a hydrogenated layer ( was calculated as follows: The SLD of a deuterated layer ( was calculated as follows: Where is mass density of the film (g/cm 3 ), is the molar fraction of water in the film, and We also took into account the inhomogeneity of thickness of LbL films that causes a smearing of the reflectivity features at higher Q values 5 by using the following formula: where is the specular reflectivity of the film using the nominal thicknesses of the LbL polymer  0 layers and and are the reflectivities of films in which the thicknesses are increased or  +  - decreased by , respectively.

Fig. S12 .
Fig. S12.The normalized autocorrelation functions for diffusion of LPMAA* (A) and 8PMAA (B) chains in 10 -2 mg/ml solutions, along with diffusion of free Alexa-488 (4 nM concentration) in 0.01 M phosphate buffer at pH 9. The solid lines represent fits with the single component 3D diffusion model.

Fig. S14 .
Fig. S14.Half-recovery time as a function of square root of apparent salt concentration (    ) in the swollen film for LPMAA*-(squares), 4PMAA* (circles), 6PMAA* (triangles), and 8PMAA*-containing (diamonds) films.The dashed lines represent linear fits to the data using the equation 4. The apparent salt concentration in the swollen film was calculated as follows:

Table S2 .
The ratio accounts for the increase in    ℎ mass density with increasing fraction of deuterated material in the H-stack.Normalized scattering length densities for polymers and water used for fitting the neutron reflectivity data.

Table S21 .
Internal roughness between H-and D-stack and the molar fraction of dQPC of the total QPC content of the H-stack ( for PMAA/QPC films at different time of annealing.w dQPC )

Table S22 .
Half-time of fluorescent recovery and diffusion coefficients obtained from FRAP experiments for linear and star PMAA/QPC films at different salt concentrations.